Horn loudspeakers consist of a loudspeaker element or driver with a horn funnel placed in front of the element. The horn serves to couple acoustic energy emitted by the element into the surrounding air, by transforming the acoustic impedance of the element to the impedance of the space. The advantages of the horn speaker compared with other speaker designs, such as bass reflex, band pass and closed systems, are a high sensitivity and a good transient response due to the good coupling properties. In addition the well controlled spreading of the sound may be exploited to avoid echo and feedback in public address systems. However, a horn speaker is a complicated construction, and it is well known that many horns designs have an inferior sound quality, with a characteristic horn sound.
FIG. 1 shows the principle followed by most horn speaker designs, with a compression chamber in front of an element leading into a horn funnel with an exponential expansion. The back of the element is closed by a small closed chamber.
The air in the closed back chamber will expand when the diaphragm (or cone) moves outward and become compressed when the cone moves inward. Thus, the air will act as an elastic spring on the cone. This is governed by the gas law pVγ=C where γ is the adiabatic exponent which is about 1.4 for air, p is pressure, V is volume, and C is a constant. This relates to adiabatic conditions (no heat transfer).
The loudspeaker affects the volume by pushing in and out and the maximum volume change is Vd=Sd Xmax where Sd is the effective cone area and Xmax is the maximum displacement of the cone. Thus the loudspeaker affects the volume, but we sense the resulting pressure variation. The gas law shows that there is a nonlinear relationship between volume and pressure.
The gas law can be linearized for small volume changes so that there is an approximate linear relationship between cone displacement and the corresponding pressure change. This is given by the compliance or inverse stiffness which is the volume change over the pressure change: C=ΔV/Δp. Its value can be found by differentiating the gas law at the value of the surrounding pressure (p0=1 atmosphere). This is the assumption of linear acoustics. In this case the air acts as a linear spring with a constant compliance.
However, for the large volume changes that can occur in horn loudspeakers at high drive levels, the nonlinearity of the pressure-volume relationship becomes important and one enters the realm of nonlinear acoustics. In this case the value of the compliance will change for positive and negative cone excursions. This is mainly an effect that affects the lower bass as cone excursion increases with lower frequency for the same sound pressure.
The compression chamber in front of the driver has as its object to compensate for this nonlinear stiffness/compliance. However, it will only work effectively over a limited range of sound pressures, and the resultant coloring of the sound is responsible for the distinct horn sound (compression and honking) disliked by many audio enthusiasts. Honking may also arise if the horn is too short.
It has been proposed to replace the closed chamber with another horn at the back that is identical to the normal front mounted horn. It is evident that such a solution will be unrealistic in most, cases due to the large volume needed. And most horn speakers are very voluminous already. Others have tried to circumvent the problem by eliminating the closed chamber altogether (Bassmaxx) and let the driver work with an open back. Then the cone is easily loaded too little, resulting in less control of its movement, and too large cone excursions at low frequencies.
However, this solution is an improvement over speakers with closed chambers, as the compliance conditions will change less with increasing sound level.
In the mid/treble range horn speakers have very narrow direction diagrams, which may be a problem in public address settings. One solution is to stack several speakers, the sub-speakers pointing in different directions. However, such an arrangement easily leads to interference between the sub-speakers, with the direction diagram breaking up into several lobes (grating lobes). This is due to the large distance between individual sub-speakers and the curved form of the wavefront of the sound leaving each sub-speaker. The sub-speakers can not be stacked as tightly as desired due to the large size of the closed chamber at the rear of each sub-speaker. Normally, the horn walls and box walls have to be separate constructions because of the too large back chamber, and this further leads to even larger distances between sub-speakers.